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The 6th generation mobile network (6G) is expected to be launched in the early 2030s. The architecture of 6G will be the convergence of space, air, ground, and undersea networks. The power and intelligence of 6G based on advanced AI techniques will realize the concept of the Industrial Internet of Things (IIoT). In this study, we conduct a comprehensive survey of 6G IIoT applications based on Federated Learning (FL), starting from introducing recent advances in FL and IIoT systems to discussing how to integrate them. In particular, we highlight the potential of FL for supporting a range of IIoT systems such as smart medical, intelligent transportation, smart cities, unmanned aerial vehicles, and smart industry. The important discussions to drive FL into IIoT applications are emphasized. Finally, we present challenges and open issues for future research to realize green and suitable FL-based IIoT applications.